Identifying ionizable species with voltammetric duty cycles

ABSTRACT

A sensor system including devices and methods for determining the concentration of an analyte in a sample is described. Input signals including amperometric and voltammetric duty cycles of excitations and relaxations may provide a shorter analysis time and/or improve the accuracy and/or precision of the analysis. The disclosed system may reduce analysis errors, thus improving measurement performance, by adjusting the potential and/or scan rate in response to output currents obtained from voltammetric scans. The disclosed system also may determine the concentration of more than one ionizable species in the sample by adjusting the potential and/or scan rate in response to output currents obtained from voltammetric scans. The multiple, determined concentrations may be used to determine the concentration of multiple analytes or to correct the concentration determined for an analyte, thus improving the measurement performance of the system.

REFERENCE TO RELATED APPLICATIONS

This application is a divisional of U.S. Nonprovisional application Ser.No. 13/552,954, filed Jul. 19, 2012, entitled “Systems, Methods, andDevices Including Amperometric and Voltammetric Duty Cycles”, which is adivisional of U.S. Nonprovisional application Ser. No. 12/501,107, filedJul. 10, 2009, entitled “Systems and Methods Including Amperometric andVoltammetric Duty Cycles”, now U.S. Pat. No. 8,262,899, which claims thebenefit of U.S. Provisional Application No. 61/079,616 entitled “Systemsand Methods Including Amperometric and Voltammetric Duty Cycles” filedJul. 10, 2008, each of which is incorporated by reference in itsentirety.

BACKGROUND

Biosensor systems provide an analysis of a biological fluid, such aswhole blood, serum, plasma, urine, saliva, interstitial, orintracellular fluid. Typically, biosensor systems have a measurementdevice that analyzes a sample contacting a sensor strip. The sample istypically in liquid form and in addition to being a biological fluid,may be the derivative of a biological fluid, such as an extract, adilution, a filtrate, or a reconstituted precipitate. The analysisperformed by the system determines the presence and/or concentration ofone or more analytes, such as alcohol, glucose, uric acid, lactate,cholesterol, bilirubin, free fatty acids, triglycerides, proteins,ketones, phenylalanine, or enzymes, in the biological fluid. Theanalysis may be useful in the diagnosis and treatment of physiologicalabnormalities. For example, a diabetic individual may use a biosensorsystem to determine the glucose level in whole blood for adjustments todiet and/or medication.

Biosensor systems may be designed to analyze one or more analytes in thesame or in different samples and may use different sample volumes. Somesystems may analyze a single drop of whole blood, such as from 0.25-15microliters (μL) in volume. Biosensor systems may be implemented usingbench-top, portable, and like measurement devices. Portable measurementdevices may be hand-held and allow for the identification and/orquantification of one or more analytes in a sample. Examples of portablemeasurement devices include the Breeze II® and Contour® meters of BayerHealthCare Diabetes Care in Tarrytown, N.Y., while examples of bench-topmeasurement devices include the Electrochemical Workstation availablefrom CH Instruments in Austin, Tex. Systems providing shorter analysistimes, while supplying the desired accuracy and/or precision, provide asubstantial benefit to the user.

In electrochemical biosensor systems, the analyte concentration isdetermined from an electrical signal generated by an oxidation/reductionor redox reaction of a measurable species. The measurable species may beionized analyte or an ionized species responsive to the analyte when aninput signal is applied to the sample. The input signal may be appliedas a single pulse or in multiple pulses, sequences, or cycles. Anoxidoreductase, such as an enzyme or similar species, may be added tothe sample to enhance the electron transfer from a first species to asecond species during the redox reaction. The enzyme or similar speciesmay react with a single analyte, thus providing specificity to a portionof the generated output signal. Examples of some specificoxidoreductases and corresponding analytes are given below in Table I.

TABLE I Oxidoreductase Analyte Glucose dehydrogenase β-glucose Glucoseoxidase β-glucose Cholesterol esterase; cholesterol oxidase CholesterolLipoprotein lipase; glycerol kinase; Triglycerides glycerol-3-phosphateoxidase Lactate oxidase; lactate dehydrogenase; Lactate diaphorasePyruvate oxidase Pyruvate Alcohol oxidase Alcohol Bilirubin oxidaseBilirubin Uricase Uric acid Glutathione reductase NAD(P)H Carbonmonoxide oxidoreductase Carbon monoxide

A mediator may be used to maintain the oxidation state of the enzyme. Inmaintaining the oxidation state of the enzyme, the mediator is ionizedand may serve as a measurable species responsive to the analyte. TableII, below, provides some conventional combinations of enzymes andmediators for use with specific analytes.

TABLE II Analyte Enzyme Mediator Glucose Glucose Oxidase FerricyanideGlucose Glucose Dehydrogenase Ferricyanide Cholesterol CholesterolOxidase Ferricyanide Lactate Lactate Oxidase Ferricyanide Uric AcidUricase Ferricyanide Alcohol Alcohol Oxidase Phenylenediamine

The mediator may be a one electron transfer mediator or a multi-electrontransfer mediator. One electron transfer mediators are chemical moietiescapable of taking on one additional electron during the conditions ofthe electrochemical reaction. One electron transfer mediators includecompounds, such as 1,1′-dimethyl ferrocene, ferrocyanide andferricyanide, and ruthenium(III) and ruthenium(II) hexaamine.Multi-electron transfer mediators are chemical moieties capable oftaking on more-than-one electron during the conditions of the reaction.Multi-electron transfer mediators include two electron transfermediators, such as the organic quinones and hydroquinones, includingphenanthroline quinone; phenothiazine and phenoxazine derivatives;3-(phenylamino)-3H-phenoxazines; phenothiazines; and7-hydroxy-9,9-dimethyl-9H-acridin-2-one and its derivatives. Twoelectron transfer mediators also include the electro-active organicmolecules described in U.S. Pat. Nos. 5,393,615; 5,498,542; and5,520,786.

Two electron transfer mediators include 3-phenylimino-3H-phenothiazines(PIPT) and 3-phenylimino-3H-phenoxazines (PIPO). Two electron mediatorsalso include the carboxylic acid or salt, such as ammonium salts, ofphenothiazine derivatives. Two electron mediators further include(E)-2-(3H-phenothiazine-3-ylideneamino)benzene-1,4-disulfonic acid(Structure I), (E)-5-(3H-phenothiazine-3-ylideneamino)isophthalic acid(Structure II), ammonium(E)-3-(3H-phenothiazine-3-ylideneamino)-5-carboxybenzoate (StructureIII), and combinations thereof. The structural formulas of thesemediators are presented below. While only the di-acid form of theStructure I mediator is shown, mono- and di-alkali metal salts of theacid are included. The sodium salt of the acid may be used for theStructure I mediator. Alkali-metal salts of the Structure II mediatoralso may be used.

Two electron mediators may have redox potentials that are at least 100mV lower, more preferably at least 150 mV lower, than ferricyanide.Other two electron mediators may be used.

Electrochemical biosensor systems typically include a measurement devicehaving electrical contacts that connect with electrical conductors inthe sensor strip. The sensor strip may be adapted for use outside, incontact with, inside, or partially inside a living organism. When usedoutside a living organism, a sample of the biological fluid may beintroduced to a sample reservoir of the sensor strip. The sensor stripmay be placed in the measurement device before, after, or during theintroduction of the sample for analysis. When in contact with the livingorganism, the sensor strip may be attached to the skin where fluidcommunication is established between the organism and the strip. Wheninside or partially inside a living organism, the sensor strip may becontinually immersed in the fluid or the fluid may be intermittentlyintroduced to the strip for analysis. The sensor strip may include areservoir that partially isolates a volume of the fluid or be open tothe fluid. When in contact with, partially inside, or inside a livingorganism, the measurement device may communicate with the sensor stripusing wires or wirelessly, such as by RF, light-based, magnetic, orother communication techniques.

The conductors of the sensor strip may be made from conductivematerials, such as solid metals, metal pastes, conductive carbon,conductive carbon pastes, conductive polymers, and the like. Theelectrical conductors typically connect to working, counter, reference,and/or other electrodes that extend into a sample reservoir. One or moreelectrical conductors also may extend into the sample reservoir toprovide functionality not provided by the electrodes.

The measurement device applies an input signal to the electricalconductors of the sensor strip. The electrical conductors convey theinput signal through the electrodes into the sample. The redox reactionof the measurable species generates an electrical output signal inresponse to the input signal. The electrical output signal from thestrip may be a current (as generated by amperometry or voltammetry), apotential (as generated by potentiometry/galvanometry), or anaccumulated charge (as generated by coulometry). The measurement devicemay have the processing capability to measure and correlate the outputsignal with the presence and/or concentration of one or more analytes inthe biological fluid. The processing capability may be in communicationwith the measurement device, but separate. Communication may beestablished using wires or wirelessly, such as by RF, light-based,magnetic, or other communication.

In coulometry, the analyte concentration is quantified by exhaustivelyoxidizing the analyte within a small volume and integrating the currentover the time of oxidation to produce the electrical charge representingthe analyte concentration. Thus, coulometry captures the total amount ofanalyte within the sensor strip. An important aspect of coulometry isthat towards the end of the integration curve of charge vs. time, therate at which the charge changes with time becomes substantiallyconstant to yield a steady-state condition. This steady-state portion ofthe coulometric curve forms a relatively flat current region, thusallowing determination of the corresponding current. However, thecoulometric method requires the complete conversion of the entire volumeof analyte to reach the steady-state condition unless the truesteady-state current is estimated from non-steady-state output. As aresult, this method may be time consuming or less accurate due to theestimation. The sample volume of the sensor strip also must becontrolled to provide accurate results, which can be difficult with amass produced device.

Another electrochemical method which has been used to quantify analytesin biological fluids is amperometry. In amperometry, current is measuredat a substantially constant potential (voltage) as a function of time asa substantially constant potential is applied across the working andcounter electrodes of the sensor strip. The measured output current isused to quantify the analyte in the sample. Amperometry measures therate at which the electrochemically active species, such as the analyteor mediator, is being oxidized or reduced near the working electrode.Many variations of the amperometric method for biosensors have beendescribed, for example in U.S. Pat. Nos. 5,620,579; 5,653,863;6,153,069; and 6,413,411.

Voltammetry is another electrochemical method that may be used toquantify analytes in biological fluids. Voltammetry differs fromamperometry in that the potential of the input signal applied across theworking and counter electrodes of the strip changes continuously withtime. The current is measured as a function of the change in potentialof the input signal and/or time. Additional information aboutvoltammetry may be found in “Electrochemical Methods: Fundamentals andApplications” by A. J. Bard and L. R. Faulkner, 1980.

Multiple methods of applying the input signal to the strip, commonlyreferred to as pulse methods, sequences, or cycles, have been used toaddress inaccuracies in the determined analyte concentration. Forexample, in U.S. Pat. No. 4,897,162 the input signal includes acontinuous application of rising and falling voltage potentials that arecommingled to give a triangular-shaped wave. Furthermore, WO 2004/053476and U.S. Patent Docs. 2003/0178322 and 2003/0113933 describe inputsignals that include the continuous application of rising and fallingvoltage potentials that also change polarity.

Electrochemical decays may be correlated with the analyte concentrationin the sample by expressing the decay with an equation describing a linerelating current with time by the natural log function (ln), forexample. Thus, the output current may be expressed as a function of timewith an exponential coefficient, where negative exponential coefficientsindicate a decay process. After the initial decrease in current output,the rate of decrease may remain relatively constant, thus becomingsteady-state, or continue to fluctuate.

The measurement performance of a biosensor system is defined in terms ofaccuracy and/or precision. Increases in accuracy and/or precisionprovide for an increase in measurement performance for the biosensorsystem. Accuracy may be expressed in terms of bias of the sensor'sanalyte reading in comparison to a reference analyte reading, withlarger bias values representing less accuracy, while precision may beexpressed in terms of the spread or variance among multiple analytereadings in relation to a mean. Bias is the difference between a valuedetermined from the biosensor and the accepted reference value and maybe expressed in terms of “absolute bias” or “relative bias”. Absolutebias may be expressed in the units of the measurement, such as mg/dL,while relative bias may be expressed as a percentage of the absolutebias value over the reference value. Reference values may be obtainedwith a reference instrument, such as the YSI 2300 STAT PLUS™ availablefrom YSI Inc., Yellow Springs, Ohio.

Many biosensor systems include one or more methods to correct the error,and thus the bias, associated with an analysis. The concentration valuesobtained from an analysis with an error may be inaccurate. The abilityto correct these inaccurate analyses may increase the accuracy and/orprecision of the concentration values obtained. An error correctionsystem may compensate for one or more errors, such as error arising whenthe measurable species concentration does not correlate with the analyteconcentration. For example, when a biosensor system determines theconcentration of a reduced mediator generated in response to theoxidation of an analyte, any reduced mediator not generated by oxidationof the analyte will lead to the system indicating that more analyte ispresent in the sample than is correct due to mediator background. Thus,“mediator background” is the bias introduced into the measured analyteconcentration attributable to measurable species not responsive to theunderlying analyte concentration.

Measurement inaccuracies also may arise when the output signal does notcorrelate to the measurable species concentration of the sample. Forexample, when a biosensor system determines the concentration of ameasurable species from output signal currents, output currents notresponsive to the measurable species will lead to the system indicatingthat more analyte is present in the sample than is correct due tointerferent current. Thus, “interferent bias” is the bias introducedinto the measured analyte concentration attributable to interferentsproducing output currents not responsive to the underlying analyteconcentration.

As may be seen from the above description, there is an ongoing need forelectrochemical sensor systems having improved measurement performance,especially those that may provide an increasingly accurate and/orprecise determination of a biological analyte concentration. Thesystems, devices, and methods of the present invention overcome at leastone of the disadvantages associated with conventional systems.

SUMMARY

A method for measuring at least one analyte in a sample includesapplying to the sample an input signal having a first duty cycleincluding an amperometric excitation and a first relaxation and a secondduty cycle including a voltammetric excitation and a second relaxationor a first duty cycle including a voltammetric excitation and a firstrelaxation and a second duty cycle including an acyclic scan and asecond relaxation. An output signal is detected that includes outputcurrents responsive to the amperometric and voltammetric excitations. Aportion of the output signal is correlated with the concentration of theat least one analyte in the sample.

A measurement device for determining the concentration of an analyte ina sample includes a signal interface including at least two contacts,and electrical circuitry establishing electrical communication betweenthe at least two contacts and a signal generator. The electricalcircuitry includes a processor in electrical communication with thesignal generator and a storage medium. The processor is operable toapply an input signal from the signal generator to the at least twocontacts. The input signal may include a first duty cycle having anamperometric excitation and a first relaxation and a second duty cyclehaving a voltammetric excitation and a second relaxation. The inputsignal may include a first duty cycle having a voltammetric excitationand a first relaxation and a second duty cycle having an acyclic san anda second relaxation. The processor is operable to detect an outputsignal at the at least two contacts. The output signal may includeoutput currents responsive to the amperometric excitation, thevoltammetric excitation, and/or the acyclic scan. The processor isoperable to correlate a portion of the output signal into aconcentration of at least one analyte in the sample.

A method for identifying an ionizable species in a sample includesapplying an input signal including an acyclic scan to the sample, wherethe acyclic scan includes a forward excitation and a reverse excitation.Detecting an output signal, the output signal including output currentsresponsive to the acyclic scan and identifying the ionizable speciesfrom the output currents responsive to the forward excitation of theacyclic scan. The method may include identifying the ionizable speciesfrom a first ratio and a second ratio of the output currents when thesecond ratio is less than 1. The first ratio may be determined from aninitial output current responsive to the forward excitation of theacyclic scan and a midpoint output current responsive to the forwardexcitation of the acyclic scan. The second ratio may be determined fromthe midpoint output current responsive to the forward excitation of theacyclic scan and a final output current responsive to the forwardexcitation of the acyclic scan.

Other systems, methods, features, and advantages of the invention willbe, or will become, apparent to one with skill in the art uponexamination of the following figures and detailed description. It isintended that all such additional systems, methods, features andadvantages be included within this description, be within the scope ofthe invention, and be protected by the claims that follow.

BRIEF DESCRIPTION OF THE DRAWINGS

The invention may be better understood with reference to the followingdrawings and description. The components in the figures are notnecessarily to scale, emphasis instead being placed upon illustratingthe principles of the invention.

FIG. 1 represents an electrochemical analytic method for determining thepresence and/or concentration of an analyte in a sample where the inputsignal is adjusted in response to the output currents from avoltammetric scan.

FIG. 2 represents the application of an input signal.

FIGS. 3A-3D represent gated amperometric input signals where multipleduty cycles were applied to the sensor strip after introduction of thesample.

FIGS. 4A-4D represent gated voltammetric input signals where thepotential is varied with time.

FIG. 4E compares cyclic and acyclic scans.

FIG. 4F represents additional acyclic scans having different starting,reversing, and ending potentials.

FIG. 5A depicts a cyclic scan from a sensor system.

FIG. 5B compares a cyclic scan to an acyclic scan, where the forwardexcitation of the acyclic scan was started near the formal potential E°′ for the redox couple.

FIG. 5C shows an acyclic scan, where the reverse scan is terminatedbefore the reverse current peak.

FIG. 5D shows a cyclic scan with an acyclic scan superimposed in the DLCregion.

FIG. 5E depicts the output currents of an acyclic scan from the ACV-3and ACV-4 acyclic scans of FIG. 4F.

FIG. 5F compares output currents from cyclic and acyclic scans.

FIG. 6A is a graph of the semi-integral corresponding to the cyclicvoltammogram of FIG. 5A.

FIG. 6B presents the semi-integral of the output current datacorresponding to the acyclic scan of FIG. 5C.

FIG. 6C presents the semi-integrals of the cyclic and acyclic scans ofFIG. 5B.

FIG. 6D shows the semi-integral and recorded current values for theacyclic scan of FIG. 5D.

FIGS. 7A-7C represent input signals including amperometric andvoltammetric duty cycles.

FIG. 8A represents an input signal having a total of five duty cycles,where a first pulse is a stepped-amperometric excitation and thefollowing four pulses combine amperometric excitations and voltammetricscans into a single multi-excitation pulse.

FIG. 8B represents an input signal having a total of eight duty cycles,where a first pulse and a second pulse are amperometric excitations andthe following six pulses combine voltammetric scans and amperometricexcitations into a single multi-excitation pulse.

FIG. 9A represents an input signal having a total of eight duty cycles.

FIG. 9B plots the output currents as a function of time obtained when ameasurement device applied the input signal of FIG. 9A to sensor stripsincluding plasma, about 55 mg/dL of glucose as the analyte, and either0, about 4 mg/dL, or about 12 mg/dL uric acid as an interferent.

FIG. 9C and FIG. 9D plot the output currents versus potential for linearand acyclic scans.

In FIG. 9E, the analysis of FIG. 9B was repeated with a plasma sampleincluding about 110 mg/dL glucose, uric acid as naturally occurring inplasma, and about 8 mg/dL acetaminophen, as an additional interferent.

FIG. 9F depicts the detail of the linear scan of the third duty cyclerevealing three separate peaks corresponding to the mediator, uric acid,and acetaminophen, respectively.

FIG. 9G depicts that as the potential of the acyclic scan changes fromabout 0.2 to about 0.3 V and back, output current values attributable tothe uric acid and acetaminophen interferents were substantiallyeliminated.

FIG. 10A represents an input signal having a total of eight duty cycles.

FIG. 10B plots the output currents as a function of time obtained when ameasurement device applied the input signal of FIG. 10A to sensor stripsincluding plasma, about 55 mg/dL or about 111 mg/dL of glucose as theanalyte, and no additional uric acid.

FIG. 10C and FIG. 10D plot the output currents versus potential forlinear and acyclic scans.

FIG. 10E plots the output currents as a function of time obtained when ameasurement device applied the input signal of FIG. 10A to sensor stripsincluding plasma, about 445 mg/dL or about 670 mg/dL of glucose as theanalyte, and no additional uric acid.

FIG. 10F and FIG. 10G plot the output currents verses potential forlinear and acyclic scans.

FIG. 11A plots the output currents as a function of time obtained when ameasurement device applied the input signal of FIG. 9A to sensor stripsincluding plasma, about 111 mg/dL of glucose as the analyte, and either8 mg/dL acetaminophen or 8 mg/dL of acetaminophen in combination with 40mg/dL dopamine as interferents.

FIG. 11B provides expansions of the output currents recorded from theacyclic scans of duty cycles 6 and 8 and from the amperometricexcitation of duty cycle 7 of FIG. 11A.

FIG. 11C provides an expansion of the output currents from the linearscan of the third duty cycle of FIG. 11A.

FIG. 11D plots the output currents versus potential from the duty cycle8 acyclic scan for the three samples.

FIG. 12A represents an input signal having a total of eight duty cycles,where duty cycles 1, 2, 4, 5, and 7 have amperometric excitations, dutycycle 3 has a linear scan, and duty cycles 6 and 8 have acyclic scans.

FIG. 12B plots the output currents as a function of time obtained when ameasurement device applied the input signal of FIG. 12A to sensor stripsincluding plasma, about 66 mg/dL of glucose as the analyte, and eitherno additional interferents or about 12 mg/dL dopamine.

FIG. 12C provides expansions of the output currents recorded from theacyclic scans of duty cycles 6 and 8 and from the amperometricexcitation of duty cycle 7.

FIG. 12D and FIG. 12E plot the output currents versus potential from theduty cycle 6 and 8 acyclic scans for two samples.

FIG. 12F plots the dose response of current as a function of the glucoseconcentrations determined for each sample from a single output current.

FIG. 12G plots the dose response of current as a function of the glucoseconcentrations determined for each sample by averaging output currents.

FIG. 13 depicts a schematic representation of a biosensor system thatdetermines an analyte concentration in a sample.

DETAILED DESCRIPTION

An electrochemical analytic sensor system determines the concentrationof an analyte in a sample, such as the glucose concentration of wholeblood. The system includes a device that applies an input signalincluding amperometric and at least one voltammetric duty cycle to thesample. The input signal may lack an amperometric duty cycle when atleast one acyclic scan duty cycle is applied to the sample. Each dutycycle includes an excitation and a relaxation. Excitations may beamperometric or voltammetric. The system adjusts amperometric and/orvoltammetric portions of the input signal in response to output currentsobtained from voltammetric portions of the input signal. The system mayadjust the input signal to reduce output currents responsive tointerferents while reducing output current non-linearity, thus,increasing measurement performance.

The system may identify the presence and/or identity of one or moreionizable species in the sample in response to output currents obtainedfrom one or more voltammetric scans. The system may identify thepresence and/or identity of one or more ionizable species in the samplein response to output currents obtained from one or more linear scans.The system may identify the presence and/or identity of one or moreionizable species in the sample in response to output currents obtainedfrom the forward excitation of one or more acyclic scans. The system mayuse derivatives and/or ratios or other methods to determine the presenceand/or oxidation potential of one or more ionizable species in thesample from output currents responsive to voltammetric scans. The systemmay select an amperometric excitation and/or acyclic scan potentialbased on ratios determined from current values obtained from acyclicscans.

By adjusting the potential of one or more amperometric excitationsand/or one or more acyclic scans in response to output currents obtainedfrom voltammetric scans, the output currents responsive to one or moreinterferents may be reduced. The output currents obtained from thevoltammetric scans also may be used to adjust the potential of one ormore amperometric excitations and/or one or more acyclic scans to reducethe non-linearity of the output currents responsive to one or moreionizable species. In relation to a conventional system that operates ata single, relatively high potential to reduce the possibility ofnon-linear response, the system may adjust the potential of one or moreexcitations to reduce non-linearity of the output currents whilereducing output currents responsive to interferents.

The output currents obtained from the voltammetric scans also may beused to adjust the potential of one or more amperometric excitationsand/or one or more acyclic scans to determine analyte concentration andfurther adjusted to determine interferent concentration. Thus, byadjusting the potential of the input signal the system can determine theconcentration of one or more ionizable species in the sample and reportor use the determined values to correct reported concentration values.By adjusting the scan rate of one or more linear or acyclic scans inresponse to output currents obtained from linear or acyclic scans, theredox potentials of two or more ionizable species may be better defined.

The system may compare the output currents from one or more amperometricexcitations to determine the concentration of analytes, interferents, orother ionizable species in the sample. The system may determine theanalyte, interferent, or other ionizable species concentration of thesample from output currents obtained from one or more acyclic scans. Thesystem may average the output currents from an acyclic scan to determinethe analyte, interferent, or other ionizable species concentration ofthe sample. The system may apply one or more data treatments, includingthose based on semi-integration, derivatives, and semi-derivatives toanalyze the data.

Amperometric duty cycles advantageously require simpler electronics andmethods to implement, but may provide very short transient decays withshort pulse widths. For example, averaging current values recordedduring the decay from a short pulse width amperometric input signal maydecrease the measurement performance of the system because ofvariability in the output currents. In contrast, voltammetric scans,either linear or acyclic may provide output currents in a finitepotential range that are relatively constant. The relative constancy ofthe voltammetric output signals may be improved when the voltammetricinput signal is within the diffusion-limited current (DLC) region of themeasurable species being excited. As the constancy of the current valuesimprove, the measurements become easier and data manipulationtechniques, such as signal averaging, may provide increases in themeasurement performance of the system.

FIG. 1 represents an electrochemical analysis 100 for determining thepresence and/or concentration of an analyte in a sample. In sampleintroduction 110, the sample is introduced to the biosensor. In redoxreaction 120, a portion of the analyte in the sample undergoes a redoxreaction. In electron transfer 130, electrons are optionally transferredfrom the analyte to a mediator. In this manner, the concentration ofionized mediator in the sample becomes responsive to the concentrationof the analyte in the sample. In input signal application 140, an inputsignal including amperometric and voltammetric duty cycles is applied tothe sample. In voltammetric output current analysis 150, output currentsresponsive to at least one voltammetric scan are analyzed to determinethe presence and/or identity of one or more contributing ionizablespecies. In input signal adjustment 160, the input signal is adjusted inresponse to the output currents from the at least one voltammetric scan.In sample determination 170, the presence and/or concentration of one ormore contributing ionizable species in the sample, such as the analyte,is determined from one or more output signals. In sample concentrationtransmission 180, the determined ionizable species concentration may bedisplayed, stored, further processed, and the like.

In the sample introduction 110, the sample is introduced to the sensorportion of the system, such as a sensor strip. The sensor strip includesat least one working and at least one counter electrode. The electrodesmay include one or more reagent layers. The working electrode mayinclude a diffusion barrier layer that is integral to a reagent layer orthat is distinct from the reagent layer. The diffusion barrier layerprovides a porous space having an internal volume where a measurablespecies may reside. A more detailed description of the implementationand use of diffusion barrier layers may be found in U.S. Patent Doc.2007/0246357, entitled “Concentration Determination in a DiffusionBarrier Layer.”

In the redox reaction 120 of FIG. 1, a portion of the analyte present inthe sample is chemically or biochemically oxidized or reduced, such asby an oxidoreductase. This occurs as the sample hydrates the reagents.Upon oxidation or reduction, electrons optionally may be transferredbetween the analyte and a mediator in the electron transfer 130. Thus,an ionized measurable species is formed, such as from the analyte or amediator. It may be beneficial to provide an initial time delay, or“incubation period,” for the reagents to react with the analyte.

In the input signal application 140 of FIG. 1, an input signal isapplied to the sample. Input signals are electrical signals, such ascurrent or potential, that change significantly in amplitude or turn onand off at a set sequence. Thus, the input signal is a sequence ofexcitations separated by relaxations. The system may apply one or moreinput signals to the sample, including those used to determine thepresence and/or concentration of the analyte and those used to determineother factors, such as the hematocrit content of the sample or theinterferent currents.

Input signals include multiple duty cycles and may have one or morepulse interval. A pulse interval is the sum of the pulse or excitationwidth and the relaxation width constituting a duty cycle. Each pulse hasan amplitude and a width. The amplitude indicates the intensity of thepotential, the current, or the like of the excitation signal. Theamplitude may be substantially constant, such as during an amperometricexcitation, or vary, such as during a voltammetric scan. The pulse widthis the time duration of the amperometric excitation or voltammetricscan. The pulse widths of an input signal may vary or be essentially thesame. Each relaxation has a relaxation width, which is the time durationof the relaxation. The relaxation widths of an input signal may vary orbe substantially the same.

By adjusting the pulse and relaxation widths of the duty cycles, gatedinput signals may improve the measurement performance of the system.While not wishing to be bound by any particular theory, this improvementin measurement performance may result from drawing the measurablespecies excited at the working electrode from the interior of adiffusion barrier layer.

Preferable input signals include at least 3, 4, 6, 8, or 10 duty cyclesapplied during less than 30, 10, or 5 seconds. More preferably, at least3 duty cycles are applied within 10 seconds. Input signals including atleast 4 duty cycles applied in less than 7 seconds are especiallypreferred at present. Preferably, the width of each excitation pulse isindependently selected from between 0.1 and 3 seconds and morepreferably from between 0.2 and 1.2 second. At present, especiallypreferred input signal pulse widths are independently selected frombetween 0.3 and 0.8 seconds. Preferable pulse intervals are in the rangeof less than 3, 2.5, or 1.5 seconds. At present, input signals havingpulse widths of 0.3 to 0.5 second and pulse intervals from 0.7 to 2seconds are especially preferred. The input signal may have other pulsewidths and intervals.

The repetitive excitation-relaxation nature of the duty cycles directlycontrast with conventional methods where voltage is continuously appliedto and current is continuously drawn from the sensor strip. For theseconventional methods, the applied voltage may have a fixed potential ormay have a potential that is swept from a positive to a negativepotential or from a positive or a negative potential to a zero potentialrelative to a reference potential. Even at a zero relative potential,these methods continuously draw current from the sensor strip during theread pulse, which permits the electrochemical reaction to continuethroughout the read pulse. Thus, in these conventional methods thereaction that produces measurable species responsive to the analyteconcentration and the diffusion of the measurable species to the workingelectrode are both affected by current during the zero potential portionof the read pulse. The input signals of the analysis 100 are markedlydifferent from conventional methods that use a single long durationpulse with multiple measurements, such as those disclosed in U.S. Pat.No. 5,243,516.

Each amperometric duty cycle includes an excitation during whichcurrents (amperage) may be measured from a sensor strip while apotential (voltage) applied to the sensor strip is maintainedsubstantially constant with time. The potential of the amperometricexcitation may be maintained within ±10%, ±5%, or ±2% with time,preferably within ±2% with time. Each voltammetric duty cycle includes alinear, cyclic, or acyclic scan during which currents (amperage) may bemeasured from the sensor strip while a potential (voltage) applied tothe strip is varied substantially linearly with time. The potential maybe maintained within ±10%, ±5%, or ±2% of linearity with time,preferably within ±2% of linearity with time. The potential may bevaried continuously with time during the voltammetric scan. The inputsignal application 140 may include an amperometric and at least onevoltammetric duty cycle. The input signal application 140 may lack anamperometric duty cycle when at least one acyclic scan duty cycle isapplied to the sample.

In voltammetric output current analysis 150, output currents responsiveto at least one voltammetric scan are analyzed to determine the presenceand/or identity of one or more ionized species. More than onevoltammetric scan may be used, and more than one type of voltammetricscan may be used. The presence and/or identity of one or more ionizablespecies in the sample may be identified in response to output currentsobtained from a linear scan, a cyclic scan, and/or the forwardexcitation of one or more acyclic scans. The ionized species may be oneor more measurable species correlated with one or more analytes in thesample or ionized interferents and the like. Derivatives, ratios, orother methods may be used to determine the presence of one or moreionizable species in the sample from output currents responsive to thevoltammetric scans.

In input signal adjustment 160, the input signal is adjusted in responseto the output currents from the at least one voltammetric scan.Amperometric excitations or voltammetric scans may be adjusted inresponse to the output currents from the at least one voltammetric scan.The adjustments may be made to reduce or eliminate interferent currentsfrom the output currents obtained from amperometric excitations oracyclic scans. The adjustment may be made to reduce or eliminatenon-linear response from output currents obtained from amperometricexcitations or acyclic scans. The adjustment may be made to determinethe concentration of one ionizable species instead of another. One ormore adjustments may be made to the input signal to address one or moreof these concerns. Thus, the system may operate at multiple potentialsresponsive to the ionizable species of a specific sample.

In sample determination 170, output signals responsive to the inputsignal are analyzed to determine the presence and/or concentration ofone or more ionizable species in the sample. The output signals mayinclude currents measured during all or part of the amperometricexcitations and/or voltammetric scans. The output signals also may ormay not include currents measured during a relaxation or part of arelaxation. The output signals also may include currents and/orpotentials monitored at the working electrode during at least a portionof the relaxation, which are not used in determining the concentrationof the analyte in the sample. As more than one ionizable species in thesample may be ionized by different portions of the input signal, thepresence, and/or concentration of multiple analytes, mediators,interferents, and the like may be determined. Additional current, time,and/or other values also may be analyzed. While the sample determination170 follows the voltammetric output current analysis 150 and the inputsignal adjustment 160 in FIG. 1, this is not required. One or moreionizable species concentrations could be determined and then modifiedwith information obtained after the input signal adjustment 160.

A more in-depth discussion of data treatments for transformingelectrochemical currents and the related digital implementations may befound in Bard, A. J., Faulkner, L. R., “Electrochemical Methods:Fundamentals and Applications,” 1980; Oldham, K. B.; “ASignal-Independent Electroanalytical Method,” Anal. Chem. 1972, 44, 196;Goto, M., Oldham, K. B., “Semi-integral Electroanalysis: Shapes ofNeopolarograms,” Anal. Chem. 1973, 45, 2043; Dalrymple-Alford, P., Goto,M., Oldham, K. B., “Peak Shapes in Semi-differential Electroanalysis,”Anal. Chem. 1977, 49, 1390; Oldham, K. B., “Convolution: A GeneralElectrochemical Procedure Implemented by a Universal Algorithm,” Anal.Chem. 1986, 58, 2296; Pedrosa, J. M., Martin, M. T., Ruiz, J. J.,Camacho, L., “Application of the Cyclic Semi-Integral Voltammetry andCyclic Semi-Differential Voltammetry to the Determination of theReduction Mechanism of a Ni-Porphyrin,” J. Electroanal. Chem. 2002, 523,160; Klicka, R, “Adsorption in Semi-Differential Voltammetry,” J.Electroanal. Chem. 1998, 455, 253.

In sample concentration transmission 160, a measurement device maydisplay, transmit by wire or wirelessly, store for future reference,further process, and/or use one or more of the determined ionizablespecies concentrations for additional calculations. For example, thevalue determined for one analyte, mediator, or interferent may bemodified with the value determined for another analyte, mediator, orinterferent to increase the measurement performance of the system.

FIG. 2 represents an input signal 200, as could be applied in 140 ofFIG. 1. In first pulse 210, the sample is electrochemically excited withthe first pulse of the input signal. In output signal generation 220, anoutput signal is generated in response to the input signal. Inrelaxation 230, the sample is allowed to relax. In combination, thepulse 210, the output signal generation 220, and the relaxation 230constitute a duty cycle 240. In second duty cycle 250, the duty cycle240 is repeated with a second pulse replacing the first pulse 210 of theinput signal 200.

In the first pulse 210 of FIG. 2, the system ionizes a ionizablespecies. The pulse may be amperometric, thus having a substantiallyconstant voltage and polarity throughout its duration. Thus, amperometrymay determine the concentration of an analyte in a sample byelectrochemically measuring the oxidation or reduction rate of aionizable species at a substantially constant potential. Conversely, thepulse may be voltammetric, thus having a potential that is changed or“scanned” in a substantially linear manner through multiple voltages ata substantially constant polarity. In this manner, voltammetry maydetermine the concentration of an analyte in a sample by measuring theoxidation or reduction rate of the ionizable species at a potentialvarying with respect to time.

In the output signal generation 220 of FIG. 2, the system generates anoutput signal in response to one or more ionizable species in the sampleand the first pulse 210 of the input signal. The output signal, such asone or more current values, may be measured continuously orintermittently and may be recorded as a function of time. Output signalsmay include those that decline initially, those that increase and thendecline, those that reach a steady-state, and those that are transient.Steady-state currents are observed when the current change with respectto time is substantially constant. Instead of conventional steady-stateor slowly decaying currents, transient (rapidly decaying) current valuesmay be obtained from input signals having multiple duty cycles.

In the relaxation 230, the sample undergoes relaxation. During therelaxation 230, the current is reduced to at least one-half the currentflow at the excitation maxima or by at least an order of magnitude inrelation to the current flow at the excitation maxima. During therelaxation 230 the current flow may be reduced to a zero current state,which may be provided by opening the circuit through the sensor strip orother means. The electrical circuit may be closed to provide anexcitation (on state) or opened to provide a relaxation (off state)mechanically, electrically, or by other methods. A zero current statedoes not include time periods when an electrical signal is present, buthas essentially no amplitude.

During the relaxation 230, an ionizing agent, such as an oxidoreductase,may react with an analyte to generate additional measurable specieswithout the effects of an electric potential. For example, a glucosebiosensor including glucose oxidase and a ferricyanide mediator asreagents will produce additional ferrocyanide (reduced mediator)responsive to the analyte concentration of the sample withoutinterference from an electric potential during the relaxation 230.

During the second duty cycle 250 of FIG. 2, the first pulse 210 isreplaced with a second pulse, which in combination with the relaxation230, provides the second duty cycle 250 of the input signal. The secondduty cycle 250 may have the same or different pulse widths and/orintervals as the first duty cycle 240. The second pulse may beamperometric or voltammetric. As for the first pulse 210, the secondpulse excites an ionizable species, which may be an ionized analyte,mediator, or interferent, for example.

While the first and second pulses may be amperometric or voltammetric,they are different. Thus, if the first pulse 210 is amperometric, thesecond pulse is voltammetric; and if the first pulse 210 isvoltammetric, the second pulse is amperometric. One or moreamperometric, voltammetric, or other pulse may precede the first pulse210, separate the first pulse 210 from the second pulse, and/or followthe second pulse. Other combinations of amperometric excitations andvoltammetric scans may be used.

FIGS. 3A-3D represent gated amperometric input signals where multipleduty cycles were applied to the sensor strip after introduction of thesample. In these representations, square-wave pulses were used; however,other wave types compatible with the sensor system and test sample alsomay be used. For example, each of the depicted excitations could includemultiple shorter duration pulses. FIG. 3A depicts a 9 duty cycle inputsignal where 0.5 second pulses are separated by 1 second open circuitdelays to give a redox intensity (RI) of 0.357 ( 5/14), where RI is thetotal excitation time divided by the sum of the total excitation timeand the total relaxation time delays for an input signal. Thus, in FIG.3A, the second duty cycle has an excitation 320 and a relaxation 330.The output signals generated from gated amperometric input signals maybe expressed as currents recorded as a function of time.

The input signal of FIG. 3A also includes a terminal read pulse 310 oflonger duration that includes an increased voltage. The increasedvoltage of this terminal read pulse provides the ability to detectspecies having a higher oxidation potential, such as control solutions.Terminal read pulses having substantially the same voltage as theexcitation pulses of the duty cycles, such as terminal read pulse 340 ofFIG. 3B also may be used. A more complete discussion regarding terminalread pulses may be found in U.S. Patent Doc. 2009/0014339, entitled“Oxidizable Species as an Internal Reference in Control Solutions forBiosensors.”

FIG. 3D represents a gated amperometric input signal where an initialpulse 360 is applied at a higher voltage than the following four pulses.In addition, the relaxation widths are varied between the initial pulse360 and the second pulse 370, when compared with the relaxation widthsof the remaining pulses. In contract to the amperometric excitations ofFIGS. 3A-3C, the amperometric excitations of FIG. 3D each include twoportions of a substantially constant voltage to provide astepped-amperometric pulse. Thus, gated amperometric input signalshaving more than one substantially constant voltage per pulse may beused.

In contrast to the amperometric excitations of FIGS. 3A-3D, FIGS. 4A-4Frepresent gated voltammetric duty cycles where the potential is variedwith time. FIG. 4A represents gated linear scans including a forwardscan 410, while FIG. 4B represents gated cyclic scans including theforward scan 410 coupled with a reversing-point 415 and a reverse scan420. A reversing-point is the point in a cyclic or acyclic scan when theforward scan is stopped and the reverse scan begins. In combination, theforward scan 410 and the reverse scan 420 may substantially cover thepotential range of a mediator, such as ferricyanide. FIGS. 4C and 4Drepresent gated acyclic scans, where in FIG. 4C the forward scan startsat a different voltage than where the reverse scan stops and in FIG. 4Dthe forward and reverse scans substantially occur in the DLC region ofone species of a redox couple, such as under the ferrocyanide species ofthe ferricyanide/ferrocyanide redox couple.

FIG. 4E compares cyclic and acyclic scans. Cyclic scan CV-1 starts at aninitial potential of −0.3 V, where the reduced species of the redoxcouple is dominant, increases to a +0.6 V reversing point potential, andreturns to the initial −0.3 V potential. Cyclic scan CV-2 starts at aninitial potential of −0.2 V, where the reduced species of the redoxcouple is dominant, increases to a +0.4 V reversing point potential, andreturns to the initial −0.2 V potential.

Acyclic scan ACV-1 starts at an initial potential of 0 V, where thereduced and oxidized species of the redox couple have similarconcentrations, increases to a +0.6 V reversing point potential, andreturns to the initial 0 V potential. Acyclic scan ACV-2 starts at aninitial potential of +0.2 V, increases to a +0.3 V reversing pointpotential, and returns to the initial +0.2 V potential. Preferably, the+0.2 V and +0.3 V potentials are within the DLC region of the redoxcouple. For example, and as determined from cyclic scan CV-1,ferrocyanide has a plateau region from approximately from +0.1 V to +0.6V when compared against the redox potential of theferricyanide/ferrocyanide redox couple. Other starting, reversing, andending potentials may be used, depending on multiple factors, such asthe redox profile of the redox couple.

FIG. 4F represents additional acyclic scans having different starting,reversing, and ending potentials. Acyclic scan ACV-3 starts at aninitial potential of −0.3 V, where the reduced species of the redoxcouple is dominant, increases to a +0.6 V reversing point potential, andreturns to a +0.1 V potential before the reverse potential scansubstantially initiates reduction of the redox couple. Acyclic scanACV-4 starts at an initial potential of −0.3 V, where the reducedspecies of the redox couple is dominant, increases to a +0.4 V reversingpoint, and returns to a +0.1 V potential before the reverse potentialscan substantially initiates reduction of the redox couple. Acyclic scanACV-5 starts at an initial potential of 0 V, where the reduced andoxidized species of the redox couple have similar concentrations,increases to a +0.6 V reversing point, and returns to an about +0.15 Vpotential before the reverse potential scan substantially initiatesreduction of the redox couple. Other starting, reversing, and endingpotentials may be used, depending on multiple factors, such as the redoxprofile of the redox couple.

During a linear scan, such as forward scan 410 depicted in FIG. 4A, thecurrent at the working electrode is measured while the potential at theworking electrode changes linearly with time at a constant rate. Thescan range, such as from −0.5 V to +0.5 V, may cover the reduced andoxidized states of a redox couple so that a transition from a firststate to a second state occurs. Redox couples are two conjugate speciesof a chemical substance having different oxidation numbers wherereduction of the species having the higher oxidation number produces thespecies having the lower oxidation number and oxidation of the specieshaving the lower oxidation number produces the species having the higheroxidation number.

A voltammogram (a plot of current versus voltage) may be characterizedby a plot that starts at an initial current, reaches a peak current, anddecays to a lower DLC level during the scan. The initial current issubstantially dependent on the applied potential, while the DLC is not.If the scan is slow enough, the DLC region may be seen as a plateauregion in a voltammogram.

The DLC region is believed to represent a state where the oxidation orreduction of the ionizable species at the conductor surface reaches amaximum rate substantially limited by diffusion. The diffusion may belimited by the rate at which the ionizable species travels from thesample to the conductor surface. Alternatively, when the workingelectrode of the sensor strip includes a diffusion barrier layer, thediffusion may be limited by the rate at which the ionizable speciestravels from the diffusion barrier layer to the conductor surface.

After completion of the forward scan 410, for a cyclic or acyclic scan,such as those depicted in FIGS. 4B and 4C-4D, respectively, a reversedpotential linear scan 420 is applied. The reversed potential linear scan420 may be applied at substantially the same rate as the forward scan410 or at a different rate. Thus, the potential is scanned from a firstlower value to a higher value and back to a second lower value, wherethe first and second lower values may or may not be the same for cyclicor acyclic scans, respectively. Cyclic, and in some instances acyclic,scans may examine the transition of a redox species from a reduced stateto an oxidized state (and vice versa) in relation to the appliedpotential or in relation to the diffusion rate of the redox species tothe conductor surface.

In relation to a linear scan, cyclic and acyclic scans may provide abetter representation of the DLC region of the scan. Cyclic and acyclicscans also may be especially advantageous for quantifying the DLC fromquasi-reversible redox couples at fast scan rates. Quasi-reversibleredox couples are redox couples where the separation between the forwardand reverse scans of the semi-integral is larger than 30 mV at thehalf-height of the si_(ss) transition for the redox couple. Additionalinformation about linear and cyclic scan voltammetry may be found in“Electrochemical Methods: Fundamentals and Applications” by A. J. Bardand L. R. Faulkner, 1980.

Poorly activated electrodes may not provide an acceptable DLC conditioneven with reversible or quasi-reversible redox couples. Thus, electrodeactivation procedures, such as those described in U.S. Pat. No.5,429,735, may be used to achieve the preferred electrode activity.

In addition to pulse width, which may be shorter as represented in FIG.4D or longer as represented in FIG. 4B, the rate (mV/sec) at which thepotential is changed (scanned) also may be varied. For gated inputsignals, voltammetric scans changing at the rate of at least 176 mV/secare preferred, with scan rates of from 200 to 5000 mV/sec being morepreferred, and scan rates of from 500 to 1500 mV/sec being especiallypreferred at present.

Gated input signals may have varying redox intensities (RI) depending onthe pulse and relaxation widths of the duty cycle. The output signalsgenerated from gated input signals may be expressed as currents recordedas a function of time. A more detailed discussion of gated amperometricinput signals may be found in U.S. Patent Doc. 2008/0173552, entitled“Gated Amperometry.” The output signals generated from gatedvoltammetric input signals may be expressed as currents recorded as afunction of the applied voltage with time. A more detailed discussion ofgated voltammetric input signals may be found in U.S. Patent Doc.2008/0179197, entitled “Gated Voltammetry.”

The higher the RI for an input signal, the less mediator backgroundinaccuracy may be introduced into the analysis by the mediator. Theinput signals represented in FIGS. 3A-3D and 4A-4C are oxidative pulses,designed to excite (e.g. oxidize) a reduced mediator, which is themeasurable species. Thus, the greater the oxidative current applied tothe sensor strip in a given time period, the less chance that mediatorreduced by pathways other than oxidation of the analyte contributes tothe recorded current values. In combination, the multiple duty cycles ofthe gated amperometric and voltammetric input signal may eliminate theneed for an initial pulse to renew the oxidation state of the mediator.For ferricyanide and the organic two electron mediators of StructuresI-III, input signals may have RI values of at least 0.01, 0.3, 0.6, or1, with RI values of from 0.1 to 0.8, from 0.2 to 0.7, or from 0.4 to0.6 being preferred. Other RI values may be used and other RI values maybe preferred for other mediators or combinations of mediators.

FIG. 5A presents the data from a 25 mV/sec cyclic scan of aferricyanide/ferrocyanide redox couple as a cyclic voltammogram, such asobtained from the CV-1 scan of FIG. 4E. The voltammogram ischaracterized by a forward current peak during the forward excitation ofthe scan from −0.3 V to +0.6 V indicating ferrocyanide oxidation and areverse current peak during the reverse voltage scan from +0.6 V back to−0.3 V indicating ferricyanide reduction. The forward and reversecurrent peaks center around the formal potential E⁰′ of theferrocyanide/ferricyanide redox couple, when referenced to the counterelectrode. In this aspect, the potential of the counter electrode issubstantially determined by the reduction potential of ferricyanide, themajor redox species present at the counter electrode.

While the potentials where the forward and reverse scans begin (the scanrange) may be selected to include the reduced and oxidized states of theredox couple, the scan range may be reduced to shorten the analysistime. However, the scan range preferably includes the DLC region for theredox couple. For example, at a scan rate of 25 mV/sec, theconcentration of the reduced [Red] and oxidized [Ox] species of theferrocyanide/ferricyanide reversible redox couple and the resultingelectrode potential are described by the Nernst equation as follows inEquation (1). Reversible redox couples are two redox species where theseparation between the forward and reverse scans of the semi-integral isat most 30 mV at the half-height of the si_(ss) transition. For example,in FIG. 6A the forward and reverse semi-integral scans for theferricyanide/ferrocyanide redox couple in addition to the si_(ss)transition height are shown. At the line where the half-height si_(ss)transition line intersects the forward and reverse scan lines theseparation between the lines is 29 mV, establishing the reversibility ofthe ferricyanide/ferrocyanide redox couple at the depicted scan rate.

$\begin{matrix}{E = {E^{0^{\prime}} + {\frac{RT}{n\; F}\ln \; \frac{\lbrack{Ox}\rbrack}{\left\lbrack {{Re}\; d} \right\rbrack}\underset{\underset{\_}{\_}}{T = {25{^\circ}\mspace{14mu} {C.}}}\mspace{14mu} E^{0^{\prime}}} + {\frac{0.059}{n}\log \; \frac{\lbrack{Ox}\rbrack}{\left\lbrack {{Re}\; d} \right\rbrack}\underset{\underset{\_}{\_}}{n = 1}\mspace{14mu} E^{0^{\prime}}} + {0.059\; \log \; \frac{\lbrack{Ox}\rbrack}{\left\lbrack {{Re}\; d} \right\rbrack}}}} & (1)\end{matrix}$

In the Nernst equation, R is the gas constant of 8.314 Joul/(mole*K), Fis the Faraday constant of 96,5000 Coul./equiv., n is the number ofequivalents per mole, and T is the temperature in degrees Kelvin. Whenthe potential at the working electrode is compared to its own redoxpotential, the formal potential E⁰′ will become substantially zero andthe equation collapses to:

$\begin{matrix}{E = {{0.059\; \log \; \frac{\lbrack{Ox}\rbrack}{\lbrack{Red}\rbrack}} = {0.059\; \log {\frac{\left\lbrack {{Fe}({CN})}_{6}^{- 3} \right.}{{{Fe}({CN})}_{6}^{- 4}}.}}}} & (2)\end{matrix}$

From equation (2), when the ratio of the oxidized mediator to thereduced mediator changes by 10, the potential at the working electrodechanges by about 60 mV. The reverse is also true. Thus, for ferricyanide[Ox] to ferrocyanide [Red] concentration ratios of 10:1, 100:1, 1000:1and 10,000:1, the potential at the working electrode will beapproximately 60, 120, 180, and 240 mV away from the zero potential,respectively.

Thus, when the ratio of ferricyanide to ferrocyanide is ˜1000:1, a scanrange of −180 mV to +180 mV would provide substantially completeoxidation of the reduced species at the working electrode. At 180 mV,the oxidation rate is limited by how fast the reduced form of themediator can diffuse to the conductor surface, and from this potentialforward, there exists a DLC region. Thus, if the reversing-point is set˜400 mV from the zero potential, ˜200 mV of DLC region may be provided.

For reversible systems, it may be preferable to provide a scan range offrom 400 to 600 mV, thus scanning from 200 to 300 mV on each side of theformal potential E⁰′ of the redox couple. For quasi-reversible systems,it may be preferable to provide a scan range of from 600 to 1000 mV,thus scanning from 300 to 500 mV on each side of the formal potentialE⁰′ of the redox couple.

The larger scan range may be preferred for quasi-reversible systemsbecause the DLC region may be smaller. In addition to redox couples thatare inherently quasi-reversible, fast scans may cause a redox couplethat is reversible at slow scan rates to demonstrate quasi-reversiblebehavior. Thus, it may be preferable to provide a largerquasi-reversible scan range for a reversible redox couple at fast scanrates.

Preferably, at least 25, 50, 100, 150, or 300 mV of DLC region isprovided by the selected scan range. In another aspect, thereversing-point for a cyclic or acyclic scan is selected so that from 25to 400 mV, from 50 to 350 mV, from 100 to 300 mV, or from 175 to 225 mVof DLC region is provided. For reversible systems, the reversing-pointfor a cyclic or acyclic scan may be selected so that from 180 to 260 mVor from 200 to 240 mV of DLC region is provided. For quasi-reversiblesystems, the reversing-point for a cyclic or acyclic scan may beselected so that from 180 to 400 mV or from 200 to 260 mV of DLC regionis provided.

Once the reversing-point is selected to provide the desired DLC region,the duration of the reverse scan may be selected for an acyclic scan. Ascan be seen in FIG. 5B, starting the forward scan and terminating thereverse scan at approximately −0.025 mV resulted in an acyclic scan,such as would be obtained from scan ACV-1 of FIG. 4E, which includedmore of the forward current peak than the reverse current peak. From theFIG. 5B comparison, while the peak currents obtained for the cyclic(CV-1) and acyclic (ACV-1) scans differ, the DLC region of the scanswere nearly the same, especially with regard to the reverse scan.

In another aspect, the reverse scan may be terminated before the reversecurrent peak is reached, as depicted in FIG. 5C. When the forward scanwas started at a potential sufficiently negative, such as at −0.3 mV inFIG. 5C, to the middle of the potential range of the redox couple, suchas −0.05 mV in FIG. 5C, the forward scan included the full range of theredox potential of the redox couple. A scan of this type would beobtained from the pulse CV-2 of FIG. 4E. Thus, by terminating thereverse excitation at a potential from 50 to 500 mV, from 150 to 450 mV,or from 300 to 400 mV negative from the reversing-point, for example,the reverse current peak may be excluded for theferricyanide/ferrocyanide redox couple.

Similarly, the reverse scan also may be terminated before the reversecurrent peak is reached by terminating the scan when the reverse scancurrent deviates in value from the DLC. A change in the reverse scancurrent of at least 2%, 5%, 10%, or 25% may be used to indicate thebeginning of the reverse scan current peak.

FIG. 5D compares a 1 V/sec cyclic voltammogram including the forward andreverse oxidation peaks of the redox couple with a 1 V/sec acyclicvoltammogram that excludes the forward and reverse oxidation peaks of aredox couple. The acyclic scan had starting and ending points of 200 mVand a reversing-point of 300 mV, as would be provided from the ACV-2acyclic scan represented in FIG. 5D. Preferable ranges for acyclic scanswithin the DLC region of the ferricyanide/ferrocyanide redox couple,which exclude the forward and reverse oxidation and reduction peaks, arefrom 10 to 200 mV, more preferably from 50 to 100 mV. While the cyclicvoltammogram including the complete scan range significantly decayedafter reaching the current peak, the acyclic voltammogram provided asubstantially flat current region over the scan range. This currentregion may be directly correlated with the analyte concentration of thesample.

As seen in FIG. 5D, the current values recorded from the acyclic scanare numerically smaller than those from the cyclic scan, while thebackground current is lower for the acyclic scan. This beneficialreduction in background current was unexpectedly obtained without havingto initiate the acyclic scan in the reduction peak portion of the cyclicscan. Thus, a fast and short acyclic scan within the DLC region of aredox couple may increase the measurement performance of the system dueto a reduction in the background current, which may provide an increasein the signal-to-background ratio.

FIG. 5E shows that the steady-state portion of the current may beindependent of the reversing point potential. FIG. 5F compares theoutput currents from the cyclic scan CV-1 from FIG. 4E with the outputcurrents from the acyclic scan ACV-5 from FIG. 4F. The figures show thatsubstantially similar steady-state currents may be obtained fromdifferent starting potentials.

FIG. 6A presents the semi-integral plot of the cyclic voltammogram fromFIG. 5A where the flat region extending from about 0.1 V to 0.6 Vdefines the DLC region or the current plateau. This plateau region isembedded in the voltammetric output currents of FIG. 5A extended fromthe peak potential into the high potentials. Similarly, FIG. 6B presentsthe semi-integral plot of the acyclic voltammogram from FIG. 5C, wherethe reverse excitation terminated before initiation of the reversecurrent peak. FIG. 6C establishes that when the semi-integral of thecyclic and acyclic scans of FIG. 5B are plotted, the DLC region of thereturn scan was readily established, permitting an accurate currentreading in as little as 50 mV from the reversing-point. Furthermore, thepeak portion of the semi-integral plot was responsive to the hematocritcontent of the sample and the magnitude of the peak may bequantitatively related to the hematocrit level.

FIG. 6D shows the semi-integrals for the cyclic and 200 to 300 mVacyclic scans of FIG. 5D. The shape of the si voltammogram from theshort acyclic scan differs from the voltammogram of the cyclic scanbecause the region of oxidation-reduction transition is missing from theacyclic scan. By starting the acyclic scan in the DLC region, thebackground si current decreased at a faster rate in comparison to thatobserved for the cyclic voltammogram, thus improving thesignal-to-background ratio for the acyclic scan. Furthermore, thereverse si current from the acyclic scan shows a plateau more accuratelydescribing the analyte concentration of the sample than the forward sicurrent. In this manner, the acyclic scan of the DLC region provided anincrease in accuracy for the analysis when compared to the cyclic scan.

Cyclic and acyclic scans may provide multiple benefits in relation tolinear scans. In one aspect, the portion of the reverse scan from thereversing-point to the point where the reverse current peak begins maybe a better representation of the true DLC values than the DLC region ofthe forward scan. The DLC region of the reverse scan may be a moreaccurate representation of analyte concentration for quasi-reversibleredox systems or at fast scan rates because the forward scan may notshow a distinct DLC region.

Acyclic scans may have multiple advantages over cyclic scans including ashorter pulse width and a substantial decrease in the amount of mediatorelectrochemically converted to the measurable state. Thus, if themediator is reduced in response to the analyte and electrochemicallyoxidized during measurement, terminating the reverse scan before theoxidized mediator is electrochemically reduced decreases the amount ofreduced mediator in the sample not responsive to the analyte. Similarly,starting the forward scan at a potential above that at which themeasurable species is reduced also may decrease the amount of reducedmediator in the sample not responsive to the analyte. Both acyclic scansmay allow for a shorter analysis time, a significant benefit for theuser.

FIGS. 7A-7C represent input signals including amperometric andvoltammetric duty cycles. The input signals also may include initialincubation periods and the like. FIG. 7A represents an input signalhaving a total of seven duty cycles, where three of the duty cyclesinclude square-wave amperometric excitations of two differentamplitudes, and four of the duty cycles include linear scans. Thevoltammetric scans are at a scan rate of 1 V/sec, requiring about 0.7seconds to complete the scan from −0.3 V to +0.4 V. The pulse width ofthe voltammetric scans is approximately equivalent to that of theamperometric scans, which have a pulse width of about 1 second. Thelinear scans cover the potential range from the substantially reduced(−0.3 V) to the substantially oxidized (+0.4 V) form of the redoxcouple, presuming the working and counter electrodes include the samecouple. The linear scan terminates at the substantially oxidizedendpoint (+0.4 V) for the couple and does not reverse.

FIG. 7B represents an input signal having a total of eight duty cycles,where three of the duty cycles include square-wave amperometricexcitations of substantially the same amplitude, and the remaining fiveduty cycles include cyclic scans, presuming the working and counterelectrodes include the same mediator. The amperometric and cyclic scanshave approximately the same scan rate of 1 V/sec, requiring about 1.4seconds to complete the scan from −0.3 to +0.4 V and back to −0.3 V. Thecyclic scans cover the potential range from the substantially reduced(−0.3 V) to the substantially oxidized (+0.4 V) form of the redoxcouple, presuming the working and counter electrodes include the samecouple; however, unlike in FIG. 7A, the voltammetric scans include areversing-point at the substantially oxidized (+0.4 V) form of thecouple and return to the substantially reduced (−0.3 V) form.

FIG. 7C represents an input signal having a total of five duty cycles,where two of the duty cycles include square-wave amperometricexcitations of substantially the same amplitude, and the remaining threeduty cycles include acyclic scans, presuming the working and counterelectrodes include the same mediator. The input signal of FIG. 7C alsoincludes an acyclic scan as a terminal read pulse, as the excitation isnot followed by a relaxation. The amperometric excitation and acyclicscans have approximately the same scan rate of 1 V/sec, requiring about0.2 seconds to complete the scan from +0.2 V to +0.3 V and back to +0.2V. As the voltammetric scans occur in the plateau region of the redoxcouple, the currents are substantially flat across the relatively short0.1 V potential range of oxidation. Voltammetric scans of this typeprovide output signals including currents representing measurablespecies lacking the relatively fast amperometric decays, but having beenexcited for relatively short time periods. Output signals of this typemay be preferred to increase the measurement performance of the system.Input signals having these and other duty cycle arrangements may be usedto increase the measurement performance of the system.

FIG. 8A represents an input signal having a total of five duty cycles,where a first pulse 860 is a stepped-amperometric excitation and thefollowing four pulses combine amperometric excitations and voltammetricscans into a single multi-excitation pulse 870. Each of themulti-excitation pulses includes an acyclic component 872 and anamperometric excitation component 874. While the acyclic scan components872 are depicted first, they could follow the amperometric excitationcomponents 874. Furthermore, more than one of each component could beincluded in the same pulse. Each of the pulses 860, 870 are followed bya relaxation to provide a duty cycle. A terminal read pulse could beused that is not followed by a relaxation. The pulse widths of theacyclic scan components 872 and the amperometric excitation components874 are approximately equal; however, one could be longer. The acyclicscan portion of the pulse may occur in the plateau region of a redoxcouple. Output signals of this type may be preferred to increase themeasurement performance of the system. Input signals having these andother duty cycle arrangements may be used to increase the measurementperformance of the system.

FIG. 8B represents an input signal having a total of eight duty cycles,where a first pulse 861 and a second pulse 862 are amperometricexcitations and the following six pulses combine voltammetric scans andamperometric excitations into a single multi-excitation pulse 870. Eachof the multi-excitation pulses starts with a linear scan component 871and transitions to an amperometric excitation component 875. While thelinear scans 871 are depicted first, they could follow the amperometricexcitations 875. Furthermore, more than one of each component could beincluded in the same pulse. Each of the pulses 861, 862, 863 is followedby a relaxation to provide a duty cycle. A terminal read pulse could beused that is not followed by a relaxation. The pulse widths of thelinear scan components 871 and the amperometric excitation components875 are approximately equal; however, one could be longer. Thevoltammetric scan component of the pulse may occur in the plateau regionof a redox couple. Output signals of this type may be preferred toincrease the measurement performance of the system. Input signals havingthese and other duty cycle arrangements may be used to increase themeasurement performance of the system.

Input signals including multiple duty cycles provide the benefits ofrapid analysis times and reductions in mediator background and thehematocrit effect. Amperometry provides output signals that may be usedfor temperature, underfill, and bias compensation, such as described inWO 2007/100651; U.S. Patent Doc. 2009/0095071, entitled “UnderfillDetection System for a Biosensor;” and U.S. Provisional App. No.61/012,716, filed Dec. 10, 2007, entitled “Slope-based Compensation,”respectively. Other compensation methods also may be implemented usingoutput currents from input signals including multiple duty cycles, suchas those that adjust the input signal in response to the output signal,as described below.

Conversely, voltammetry provides output signals that may be integratedto strengthen the signal even with fast scan rates, thus providing ananalyte responsive signal having an enhanced signal to noise ratio evenat low analyte concentration levels in the sample. Other datatreatments, including semi-integrals, derivatives, and semi-derivativesalso may be advantageously used to process voltammetric output signals.A more detailed description of these data treatments may be found in WO2007/040913. Voltammetry also may provide qualitative data about theionizable species in the sample. Both the amperometric and voltammetricoutputs can be used independently to determine one or more analyteconcentrations. Either may be averaged or otherwise manipulated toincrease the measurement performance of the system. The amperometric andvoltammetric outputs for the same analyte also may be compared todetermine a concentration value having enhanced accuracy and/orprecision.

FIG. 9A represents an input signal having a total of eight duty cycles,where duty cycles 1, 2, 4, 5, and 7 have amperometric excitations, dutycycle 3 has a linear scan, and duty cycles 6 and 8 have acyclic scans.The number of each duty cycle is printed above the associated excitationin the figure. The amperometric excitation for duty cycle 1 was appliedat a voltage of about 1 V, while the amperometric excitation for dutycycle 2 was applied at a voltage of about 0.2 V. The amperometricexcitations for duty cycles 4, 5, and 7 were applied at a voltage ofabout 0.25 V. The linear scan rate was about 0.5 V/sec from 0 to about0.7 V. The acyclic scan rate was about 1 V/sec from about 0.2 V to areversing point of about 0.3 V and back. The acyclic scans were appliedat potentials falling within the DLC region of the Structure I mediator,which has a DLC region from about 300 to about 500 mV. Other inputsignals having different numbers and types of duty cycles, potentials,and scan rates may be used. For example, a cyclic scan could besubstituted for the linear scan.

FIG. 9B plots the output currents as a function of time obtained when ameasurement device applied the input signal of FIG. 9A to sensor stripsincluding plasma, about 55 mg/dL of glucose as the analyte, and either0, about 4 mg/dL, or about 12 mg/dL uric acid as an interferent. Otheranalytes and interferents may be used. The sensor strip included workingand counter electrodes, glucose dehydrogenase as an oxidoreductase, andthe organic, two-electron mediator of Structure I, which has a redoxpotential about 200 mV lower than ferricyanide. Other sensor stripdesigns and reagents may be used.

The input signal voltages at the working electrode relative to thecounter electrode corresponding to the output currents are representedby flat (amperometric) or angled lines (voltammetric) superimposed tothe right or above the output currents of each duty cycle for clarity.As seen in the currents obtained from the linear scan, the left shoulderof the output currents from the linear scan are responsive to themediator concentration of the sample, and the right shoulder of theoutput currents from the linear scan are responsive to the uric acidconcentration of the sample.

FIG. 9C and FIG. 9D plot the output currents versus potential for thelinear scan of duty cycle 3 and the acyclic scan of duty cycle 6,respectively. The dashed vertical line in FIG. 9C indicates the 0.25 Vpotential used for the amperometric excitations of duty cycles 4, 5, and7. In FIG. 9C, peak 910 is attributable to oxidation of the mediator andis responsive to the analyte, while peak 920 is attributable to uricacid oxidation and is responsive to the interferent. The output currentsshow that a valley occurs at about 0.3 to 0.4 V between the peakattributable to the mediator at about 0.18 V and the peak attributableto uric acid at about 0.58 V, which allows the system to determine thatat least two contributing ionizable species are present in the sample.Derivatives of the output currents from the linear scan may be used todetermine the peaks and valleys as the derivatives of the output currentvalues would be positive or negative as the currents increase ordecrease, respectively. One method of using derivatives to determine thepeaks and valleys is the sequential differentiation of data points frombeginning to ending, for instance x_(n)−x_(n-1), or x₂−x₁, x₃−x₂, x₄−x₃. . . . Thus, as the differentials change sign from positive to negativein a finite range, a peak is indicated, or a valley is indicated whenthe differential sign changes from negative to positive. Other mediatorsand interferents may provide different peaks and valleys. Othermathematical methods may be used to determine the peaks and valleys inthe output currents.

By using potentials of less than about 0.4 V for the amperometricexcitations or acyclic scans with the Structure I mediator, currentvalues attributable to the uric acid interferent may be reduced orsubstantially eliminated. Thus, the system can use the output currentsfrom the linear scan of the third duty cycle to adjust the potential ofone or more amperometric excitations or acyclic scans, thereby reducingoutput currents responsive to an interferent.

With regard to the currents obtained from the linear scan of FIG. 9B,the measurement device applied the amperometric excitations of dutycycles 5 and 7 at about 0.25 V to substantially exclude uric acidinterference. Thus, using a correlation equation or other means torelate the output currents from amperometric duty cycles 5 and/or 7 withthe analyte concentration of the sample provides an increase inmeasurement performance and a reduction in uric acid interferent bias incomparison to an analysis where the potential exceeds about 0.3 V. Thesystem can make other adjustments to the amperometric excitations oracyclic scans in response to the output currents from the linear scan toimprove the measurement performance of the system.

Alternatively, if uric acid were the analyte of interest, the outputcurrents from the linear scan may be used to adjust the potential of oneor more subsequent amperometric excitations or acyclic scans to apotential of about 0.6 V, thus obtaining output currents responsive tothe mediator and the uric acid. The output current values obtained frompotentials of less than about 0.4 V could then be subtracted from theoutput current values obtained at about 0.6 V to obtain the currentvalues substantially responsive to the uric acid concentration, whileexcluding the output current values substantially responsive to themediator. This comparison through subtraction or other methods may beperformed on the output current values or on concentration or othervalues determined from the output current values using correlationequations and the like.

As ionizable species having lower oxidation potentials produce outputcurrents at lower and higher potentials, but ionizable species havinghigher oxidation potentials do not significantly produce output currentsat lower potentials, the concentrations of one or more ionizable speciesmay be determined by subtraction or related mathematical techniques thatremove the output currents of one or more lower potential species fromhigher potential species. Thus, the system can determine theconcentration of one or more ionizable species in the sample and reportor use the determined values to correct reported concentration values.

In FIG. 9D, as the potential of the acyclic scan of duty cycle 6 wasfrom about 0.2 V to about 0.3 V and back, the output currents responsiveto the uric acid interferent were substantially eliminated. This wasestablished by the substantial overlap of the output currents from thethree acyclic scans. Thus, the output currents from acyclic scans withscan ranges from about 0.2 V to about 0.3 V and back were notsubstantially affected by the uric acid interferent and could becorrelated with the concentration of the mediator, and thus the analyte,in the sample.

In FIG. 9E, the analysis as previously described with regard to FIG. 9Bwas repeated with a plasma sample including about 110 mg/dL glucose,uric acid as naturally occurring in plasma, and about 8 mg/dLacetaminophen, as an additional interferent. In FIG. 9F, the detail ofthe linear scan of the third duty cycle reveals three separate peaks,910, 920, and 930, corresponding to the mediator, uric acid, andacetaminophen, respectively. In FIG. 9G, as the potential of the acyclicscan changes from about 0.2 to about 0.3 V and back, output currentvalues attributable to the uric acid and acetaminophen interferents weresubstantially eliminated. As previously discussed with regard to FIG.9D, the single ionizable species contributing to the output currents isreflected by the substantial overlap of the output currents from the twoacyclic scans. Thus, the output currents from acyclic scans with scanranges from about 0.2 V to about 0.3 V and back were not substantiallyaffected by the uric acid and acetaminophen interferents and could becorrelated with the concentration of the mediator, and thus the analyte,in the sample.

FIG. 10A represents an input signal having a total of eight duty cycles,where duty cycles 1, 2, 4, 5, and 7 have amperometric excitations, dutycycle 3 has a linear scan, and duty cycles 6 and 8 have acyclic scans.The amperometric excitation for duty cycle 1 was applied at a voltage ofabout 0.4 V, while the amperometric excitation for duty cycle 2 wasapplied at a voltage of about 0.2 V. The amperometric excitations forduty cycles 4, 5, and 7 were applied at a voltage of about 0.25 V. Incomparison to FIG. 9A, the scan rate of the linear scan of FIG. 10A wasat a faster rate, about 1 V/sec, while covering the same scan range from0 to about 0.7 V. The acyclic scans were applied at a rate of about 1V/sec from about 0.2 V to a reversing point of about 0.3 V and back,thus having a pulse width of about 0.1 V. Other input signals havingdifferent numbers and types of duty cycles, potentials, and scan ratesmay be used. For example, a cyclic scan could be substituted for thelinear scan.

FIG. 10B plots the output currents obtained as a function of time when ameasurement device applied the input signal of FIG. 10A to sensor stripsincluding plasma, about 55 mg/dL or about 111 mg/dL of glucose as theanalyte, and no additional uric acid. Other analytes and may be used.The sensor strip included working and counter electrodes, glucosedehydrogenase as an oxidoreductase, and used the organic, two-electronmediator of Structure I. The input signal voltages at the workingelectrode relative to the counter electrode corresponding to the outputcurrents are represented by flat (amperometric) or angled lines(voltammetric) superimposed to the right or above the output currents ofeach duty cycle for clarity. While additional uric acid was not added tothe samples, the right shoulder of the output currents from the linearscan establishes that uric acid is naturally found in blood.

FIG. 10C and FIG. 10D plot the output currents versus potential for thelinear scan of duty cycle 3 and the acyclic scan of duty cycle 8,respectively. The dashed vertical line in FIG. 10C indicates the 0.25 Vpotential used for the amperometric excitations of duty cycles 2, 4, 5,and 7. In FIG. 10C, peaks 1010 are attributable to oxidation of themediator, and are responsive to the analyte, while peaks 1020 areattributable to another oxidizable species, likely uric acid, aspreviously discussed. Both mediator peaks 1010 reach a maxima before0.15 V at the working electrode in relation to the counter electrode.The output currents show that a valley occurs at about 0.3 to 0.4 Vbetween the peak attributable to the mediator at about 0.15 V and thepeak attributable to uric acid at about 0.6 V, which as previouslydiscussed, allows the system to determine that at least two ionizablespecies are contributing to the output currents and are present in thesample.

FIG. 10D showed that the acyclic scan of duty cycle 6 produced outputcurrents that were separated with regard to the X-axis, allowing for thediffering concentrations of the mediator, and thus the analyte, to bedetermined. As the amperometric excitations were applied at 0.25 V, themeasurement device also may determine the analyte concentration of thesample from the output currents obtained from one or more of theamperometric duty cycles.

FIG. 10E plots the output currents obtained as a function of time when ameasurement device applied the input signal of FIG. 10A to sensor stripsincluding plasma, about 445 mg/dL or about 670 mg/dL of glucose as theanalyte, and no additional uric acid. In contrast to FIG. 10B, FIG. 10Edepicts non-linear output currents from the acyclic scans of duty cycles6 and 8, as the output currents from the forward excitations of theacyclic scans increase with potential. This increase with potential maybe seen as the relatively flat, but still increasing, portion 1030 ofthe output currents obtained before the reversing point of the acyclicscans of duty cycles 6 and 8.

FIG. 10F and FIG. 10G plot the output currents verses potential for thelinear scan of duty cycle 3 and the acyclic scan of duty cycle 6,respectively. The dashed vertical lines in FIG. 10F and FIG. 10Gindicate the 0.25 V potential used for the amperometric excitations ofduty cycles 4, 5, and 7. In contrast to FIG. 10C, which provided theresults from the lower 55 and 111 mg/dL glucose concentrations, in FIG.10F the oxidation peaks of the mediator responsive to the higher 445 and670 mg/dL glucose concentrations have shifted significantly to the rightin relation to the 0.25 V potential. As the peak redox potentialobserved in FIG. 10F (about 0.28 V for the 670 mg/dL sample) is greaterthan the potential of the amperometric excitations, the output currentsobtained from the amperometric excitations, such as those obtained fromduty cycles 4 and 5 in FIG. 10E, will have a non-linear response.

As the DLC region of the mediator has shifted to a higher potential, the0.2 V to 0.3 V range of the acyclic scans occur substantially beforeand/or during the oxidation peak of the mediator. Thus, the outputcurrents from acyclic scan duty cycles 6 and 8 occur substantially afterthe oxidation peak of the mediator in FIG. 10B and substantially beforeand/or during the oxidation peak of the mediator in FIG. 10E. As theacyclic scan range of FIG. 10E does not substantially fall in the DLCregion of the mediator after the oxidation peak, instead falling withinthe peak region, the output currents obtained from the forwardexcitation of the acyclic scans (potential increasing) increase with theincreasing input potential. Thus, the output currents obtained from theacyclic scans of duty cycles 6 and 8 also will have a non-linearresponse.

The system may detect a non-linear response from the slopes of theoutput currents obtained from the forward excitation of acyclic scans. Acomparison of the output currents 1050 from the forward acyclic scanlines of FIG. 10D with the output currents 1055 from the forward acyclicscan lines of FIG. 10G, show that the output currents 1055 of FIG. 10Ghad a substantially positive slope in relation to the output currents1050 of FIG. 10D. This established that for the higher 445 and 670 mg/dLglucose concentrations, the output currents obtained from the acyclicscans are not substantially from the DLC region of the mediator, but areinstead responsive to the changing potential of the acyclic scan. Thus,the forward scan portion (potential increasing) of the acyclic scans canprovide similar qualitative data as obtained from the linearscans—allowing the acyclic scans to provide output currents that the canbe used to determine the presence of non-linear response at one or morepotentials.

Depending on the severity of the non-linear response, the system may endthe analysis or adjust the potential of amperometric excitations and/oracyclic scans in response to the output currents obtained from one ormore voltammetric scans to reduce the non-linearity of the currentsobtained from the adjusted amperometric excitations and/or acyclicscans. In this manner the system may adjust the potential ofamperometric and/or acyclic scans into the DLC region of one or moreionizable species.

After determining the peak oxidation current for one or more ionizablespecies, the operating potential for subsequent excitations may beadjusted to be at least 50 mV or at least 100 mV higher than thepotential at the oxidation peak. This adjustment may reduce thenon-linearity of the output currents obtained from the subsequentexcitations and increase the measurement performance of the system.Thus, with regard to the relatively high glucose concentrations of FIG.10E through 10G, the data from the linear and/or acyclic scans may beused to increase the input potential of subsequent amperometricexcitations and/or the starting potential of subsequent acyclic scans togreater than about 0.3 V to reduce the non-linearity of the outputcurrents. Other amperometric input potentials may be used to reduce thenon-linearity of the output currents depending on the system, sample,sensor strip, and the like.

In FIG. 9 and FIG. 10 uric acid and acetaminophen interferents were usedthat have oxidation potentials that do not substantially overlap withthe oxidation potential of the Structure I, II, or III mediators. Incontrast, FIG. 11A plots the output currents obtained as a function oftime when a measurement device applied the input signal of FIG. 9A tosensor strips including plasma, about 111 mg/dL of glucose as theanalyte, and either 8 mg/dL acetaminophen or 8 mg/dL of acetaminophen incombination with 40 mg/dL dopamine as interferents. Other analytes andinterferents may be used. The oxidation potential of dopamine isslightly higher than that of the Structure I, II, or III mediators andoverlaps with the oxidation potential of acetaminophen. The sensor stripincluded working and counter electrodes, glucose dehydrogenase as anoxidoreductase, and the organic, two-electron mediator of Structure I.Other sensor strip designs and reagents may be used.

FIG. 11B provides expansions of the output currents recorded from theacyclic scans of duty cycles 6 and 8 and from the amperometricexcitation of duty cycle 7. As previously discussed, the acetaminopheninterferent is not substantially visible in the current values recordedfrom the amperometric excitation of duty cycle 7, and is not adverselyaffecting the measurement performance of the system with relation toanalyte concentrations determined from this amperometric duty cycle.However, the current values recorded from the amperometric excitation ofduty cycle 7 show a relatively small contribution 1160 from dopamine atthe right of the decay. Thus, a glucose concentration determined fromthis peak for a sample including acetaminophen would show substantiallyno interferent bias due to the acetaminophen, but would show someinterferent bias if the sample included dopamine.

FIG. 11C plots the output currents verses potential for the linear scanof duty cycle 3 from FIG. 11A. The dashed vertical line indicates the0.25 V potential used for the amperometric excitations of duty cycles 4,5, and 7. For the sample including the additional acetaminophen, outputcurrents obtained substantially overlap with those obtained from the 0addition sample until about 0.45 V—well beyond the 0.25 V potential ofthe amperometric excitation of duty cycle 7. In contrast, for the sampleincluding additional acetaminophen and dopamine, the onset of outputcurrents attributable to dopamine were observed at about 0.22 V, thuswithin the output currents obtained at the 0.25 V potential of theamperometric excitation of duty cycle 7. As previously described withregard to FIG. 11B, some interferent bias from dopamine would be presentin a glucose concentration determined from output currents obtained froma 0.25 V amperometric excitation.

FIG. 11D plots the output currents versus potential from the duty cycle6 acyclic scan for the three samples. While the output currents from theforward excitation of the acyclic scans for the 0 addition sample andthe sample including additional acetaminophen show a continuingdecrease, the current values from the sample with additionalacetaminophen and dopamine initially decrease and then increase. Thus,the forward excitation of the acyclic scan shows the presence of outputcurrents responsive to a second contributing ionizable species, in thiscase the dopamine interferent, within the about 0.2 V to about 0.3 Vscan range from the initial down and then up output current values. Thesystem can detect the presence of additional ionizable speciescontributing to the output currents within the range of the forwardexcitation of an acyclic scan from the inflection in the current values.

Ratios provide one method to determine the presence of one or morecontributing ionizable species from the output currents of the acyclicscans. A first ratio may be determined from the initial and the midpointoutput current values of the forward acyclic scan (R₁=initial outputcurrent/midpoint output current). A second ratio may be determined fromthe midpoint and the reversing point output currents of the forwardacyclic scan (R₂=midpoint output current/reversing point outputcurrent). If the two ratios are greater than one, then one contributingionizable species is present. Conversely, if the first ratio is greaterthan one and the second ratio is less than one, at least twocontributing ionizable species are present. In addition to ratios, othertechniques may be used to compare the output currents obtained from theacyclic scan duty cycles, such as derivatives, integrals, patternrecognition methods, and the like, to determine if more than oneionizable species is observed by the acyclic scan.

In the FIG. 11D acyclic scans, the output currents from the samplelacking acetaminophen and dopamine interferents have a first ratio of1.65 (7.36/4.47 uA) and a second ratio of 1.26 (4.47/3.54 uA). As bothratios are greater than one, the presence of a single contributingionizable species, in this case the mediator, is indicated. The firstand second ratios for the output currents from the sample includingacetaminophen as an interferent also are both greater than one. As bothratios are greater than one, the presence of a single contributingionizable species, again the mediator, is indicated. As confirmed inFIG. 11B and FIG. 11C, additional acetaminophen has little if any effecton the bias of the analyte concentration determined using amperometricexcitations at a potential of 0.25 V. The output currents from thesample including acetaminophen and dopamine have a first ratio of 1.26(4.35/3.37 uA) and a second ratio of 0.79 (3.37/4.27 uA). As the secondratio is less than one, at least two contributing ionizable species arepresent. Thus, output currents recorded over a scan range from 0.2 V to0.3 V would provide a glucose concentration including a bias fromdopamine.

As the acyclic scan establishes that two contributing ionizable speciesare present in the 0.2 V to 0.3 V scan range, the maximum potential ofsubsequent acyclic scans may be reduced until the second ratio increasesabove one, thus reducing output currents responsive to the dopamineinterferent and the interferent bias present in the glucoseconcentration. As previously discussed, the linearity of the outputcurrent values may be monitored as the potentials are reduced to selectan acyclic scan range or amperometric excitation potential that balancesthe negative effects of non-linear response and interferent bias.Acyclic scans may be preferred to determine the presence and/orpotentials of one or more contributing ionizable species. Amperometricexcitations may be preferred to provide output current values withreduced non-linearity and interferent bias for concentrationdetermination. As amperometric excitations are applied at asubstantially constant, single potential, the single potential value ofthe amperometric excitations has a greater likelihood of being lowenough to reduce output currents responsive to interferents while beinghigh enough to reduce non-linearity. Any combination of linear oracyclic scans may be used to determine the presence and/or potentials ofthe contributing ionizable species and/or the non-linearity of theoutput currents at a potential or a potential range.

FIG. 12A represents an input signal having a total of eight duty cycles,where duty cycles 1, 2, 4, 5, and 7 have amperometric excitations, dutycycle 3 has a linear scan, and duty cycles 6 and 8 have acyclic scans.The amperometric excitations for duty cycles 4, 5, and 7 were applied ata voltage of about 0.25 V. The linear scan rate was about 1 V/sec from 0to about 0.7 V. The acyclic scan of duty cycle 6 had a scan rate ofabout 1 V/sec from about 0.15 V to about 0.25 V and back. The acyclicscan of duty cycle 8 had a scan rate of about 1 V/sec from about 0.2 Vto about 0.3 V and back. Other input signals having different numbersand types of duty cycles, potentials, and scan rates may be used. Forexample, a cyclic scan could be substituted for the linear scan.

FIG. 12B plots the obtained output currents as a function of time when ameasurement device applied the input signal of FIG. 12A to sensor stripsincluding plasma, about 66 mg/dL of glucose as the analyte, and eitherno additional interferents or about 12 mg/dL of dopamine. Other analytesand interferents may be used. The sensor strip included working andcounter electrodes, glucose dehydrogenase as an oxidoreductase, and theorganic two electron mediator of Structure I. Other sensor strip designsand reagents may be used.

FIG. 12C provides expansions of the output currents recorded from theacyclic scans of duty cycles 6 and 8 and from the amperometricexcitation of duty cycle 7. As seen by dopamine peaks 1230 (the mediatoris peaks 1210), the acyclic scan of duty cycle 6 at the lower 0.15 to0.25 V potential includes less current responsive to dopamine than theacyclic scan of duty cycle 8 at the higher 0.2 V to 0.3 V potential. The0.25 V potential of the amperometric excitation of duty cycle 7 producedoutput currents including dopamine as seen in the middle peak, thusreducing the accuracy of an analyte concentration determined from theseoutput currents (an approximately 15% to 20% positive bias in theglucose concentration determined from the output currents of theamperometric scan is estimated from the dopamine interferent). Thiswould be expected from a 0.25 V input potential in view of the outputcurrents obtained from the acyclic scans.

FIG. 12D and FIG. 12E plot the output currents versus potential from theduty cycle 6 and 8 acyclic scans for the two samples. As previouslydiscussed, ratios may be used to determine the presence of one or morecontributing ionizable species from the output currents of the acyclicscans. From the lower potential acyclic scans of FIG. 12D, the outputcurrents from the sample lacking dopamine have a first ratio of 1.65(3.6/2.2 uA) and a second ratio of 1.22 (2.2/1.79 uA). As both ratiosare greater than one, the presence of a single contributing ionizablespecies, in this case the mediator, is indicated. The output currentsfrom the sample including dopamine have a first ratio of 1.63 (3.77/2.31uA) and a second ratio of 0.95 (2.31/2.43 uA). As the second ratio isless than one, the presence of a second contributing ionizable species,in this case the dopamine interferent, is indicated. However, the secondratio of 0.95 is nearly one, indicating that for the 0.15 V to 0.25 Vpotential range the interferent influence on the analysis is relativelyminimal. Thus, the 0.15 V to 0.25 V potential range may be selected foramperometric excitations if this range provides the ratio closest to oneof the potentials scanned.

In FIG. 12E, from the 0.2 to 0.3 V potential scans, the output currentsfrom the sample lacking dopamine have a first ratio of 1.99 (4.18/2.1uA) and a second ratio of 1.23 (2.1/1.7 uA). As both ratios are greaterthan one, the presence of a single contributing ionizable species, inthis case the mediator, is indicated. The output currents from thesample including dopamine as an interferent have a first ratio of 1.7(4.56/2.67 uA) and a second ratio of 0.91 (2.67/2.95 uA). As the secondratio is less than one, the presence of a second contributing ionizablespecies, in this case the dopamine interferent, is indicated. When thesecond ratio of the higher potential acyclic scan (0.91) is compared tothe second ratio of the lower potential acyclic scan (0.95), thepotential of the amperometric excitation may be selected from the lowerpotential scan range, as the lower potential more effectively excludesoutput currents responsive to the dopamine interferent.

The input signal of FIG. 12A also was applied to whole blood samplesincluding multiple known concentrations of glucose at hematocrit levelsof 25%, 40%, or 55% (v/v). A YSI reference instrument was used todetermine the reference (known) glucose concentration of each sample.FIG. 12F plots the dose response of a single output current as afunction of the known glucose concentrations for each sample. The singleoutput current was taken from the amperometric excitation of duty cycle5. FIG. 12G plots the dose response of averaged output currents as afunction of the known glucose concentrations for each sample. Theaveraged output currents were determined by averaging the outputcurrents obtained from the acyclic scan of duty cycle 6.

As seen below in Table III, a slight increase was observed in the R² ofthe concentration values when the averaged output currents were comparedto the single output current. Thus, the glucose concentrationsdetermined from averaging the output currents from the acyclic scan werecomparable to the glucose concentrations determined from a single outputcurrent from the acyclic scan. The averaged output currents from theacyclic scan provided some increase in the sensitivity of the system asobserved from the increase in the slope values of the correlation lines.Increases in the numerical value of the slope reflect an increase in thecorrelation between the output currents and the actual analyteconcentration of the sample. Thus, analyte concentrations can bedetermined from single output currents and/or from output currentscombined through averaging and the like. The single or averaged outputcurrent values may be used to determine the concentration of one or moreanalytes in the sample using one or more data treatments and/orcorrelation equations. While the preceding description addresses inputsignals including amperometric and at least one voltammetric duty cycle,the amperometric excitation could be substituted with an acyclic scanfrom which the analyte concentration also may be determined. Thus, theinput signal does not require an amperometric duty cycle. Additionalinformation regarding the determination of analyte concentrations fromgated voltammetric input signals may be found in U.S. Patent Doc.2008/0179197, entitled “Gated Voltammetry.”

TABLE III 25% 40% 55% Hematocrit Hematocrit Hematocrit Single Current R²0.9957 0.9966 0.9972 Single Current Slope 0.0223 0.0191 0.0163 AveragedCurrents R² 0.9964 0.9957 0.9988 Averaged Currents 0.0256 0.0222 0.0195Slope

While not shown in the figures, if the system determines from the outputcurrents obtained from the voltammetric scans that more than onecontributing ionizable species is present in the sample, the system canreduce the scan rate of a voltammetric scan to better define the outputcurrents. For example, if closely spaced peaks are present in the outputcurrents from a linear scan, the scan rate could be reduced from 1 V/secto 0.5 V/sec to increase the output current resolution in the potentialrange of interest. Other scan rates may be selected.

FIG. 13 depicts a schematic representation of a biosensor system 1300that determines an analyte concentration in a sample of a biologicalfluid using an input signal including amperometric and at least onevoltammetric duty cycle. The input signal may lack the amperometric dutycycle when at least one acyclic scan duty cycle is applied to thesample. Biosensor system 1300 includes a measurement device 1302 and asensor strip 1304, which may be implemented in any analyticalinstrument, including a bench-top device, a portable or hand-helddevice, or the like. The biosensor system 1300 may be utilized todetermine analyte or interferent concentrations, including those ofalcohol, glucose, uric acid, lactate, cholesterol, bilirubin, free fattyacids, triglycerides, proteins, ketones, phenylalanine, enzymes,acetaminophen, dopamine, and the like. While a particular configurationis shown, the biosensor system 1300 may have other configurations,including those with additional components.

Measurement device 1302 and sensor strip 1304 may be adapted toimplement an electrochemical sensor system or a combinationelectrochemical/optical sensor system. The combined amperometric andvoltammetric duty cycles may improve the accuracy and/or precision ofthe biosensor system 1300 by reducing output currents obtained frominterferents, or may allow the biosensor system 1300 to determine theconcentration of more than one ionizable species. While a particularconfiguration is shown, biosensor system 1300 may have otherconfigurations, including those with additional components.

The sensor strip 1304 has a base 1306 that forms a reservoir 1308 and achannel 1310 with an opening 1312. The reservoir 1308 and the channel1310 may be covered by a lid with a vent. The reservoir 1308 defines apartially-enclosed volume. The reservoir 1308 may contain a compositionthat assists in retaining a liquid sample such as water-swellablepolymers or porous polymer matrices. Reagents may be deposited in thereservoir 1308 and/or channel 1310. The reagents may include one or moreenzymes, enzyme systems, mediators, binders, and like species. Thesensor strip 1304 also may have a sample interface 1314 disposedadjacent to the reservoir 1308. The sample interface 1314 may partiallyor completely surround the reservoir 1308. The sensor strip 1304 mayhave other configurations. For example, the sensor strip 1304 may beadapted for transdermal use by forming the reservoir 1308 from a porousmaterial or behind a porous material in which the sample is held.

The sample interface 1314 has conductors connected to at least oneworking electrode and at least one counter electrode. The electrodes maybe substantially in the same plane or in more than one plane, such aswhen facing. The electrodes may be disposed on a surface of the base1306 that forms the reservoir 1308. The electrodes may extend or projectinto the reservoir 1308. A dielectric layer may partially cover theconductors and/or the electrodes. The counter electrode may be used tobalance the potential at the working electrode during the analysis. Thebalancing potential may be provided by forming the counter electrodefrom an inert material, such as carbon, and including a soluble redoxspecies, such as ferricyanide, within the reservoir 1308. Alternatively,the balancing potential may be a reference potential achieved by formingthe counter electrode from a reference redox couple, such as Ag/AgCl, toprovide a combined reference-counter electrode. The sample interface1314 may have other electrodes and conductors. Sample interface 1314 mayhave one or more optical portals or apertures for viewing the sample.Sample interface 1314 may have other components and configurations.

The measurement device 1302 includes electrical circuitry 1316 connectedto a sensor interface 1318 and a display 1320. The electrical circuitry1316 includes a processor 1322 connected to a signal generator 1324, anda storage medium 1328. Measurement device 1302 may have other componentsand configurations.

The signal generator 1324 provides an electrical input signal to thesensor interface 1318 in response to the processor 1322. The electricalinput signal may be transmitted by the sensor interface 1318 to thesample interface 1314 to apply the electrical input signal to the sampleof the biological fluid. The electrical input signal may be a potentialor current and may be constant, variable, or a combination thereof, suchas when an AC signal is applied with a DC signal offset. The electricalinput signal may be applied as a single pulse or in multiple pulses,sequences, or cycles. The electrical input signal may includeamperometric and at least one voltammetric duty cycle. The electricalinput signal may lack an amperometric duty cycle when at least oneacyclic scan duty cycle is applied to the sample. The electrical inputsignal may include at least three amperometric and at least two acyclicscan duty cycles. The signal generator 1324 also may record an outputsignal from the sensor interface as a generator-recorder.

The storage medium 1328 may be a magnetic, optical, or semiconductormemory, another processor readable storage device, or the like. Thestorage medium 1328 may be a fixed memory device, a removable memorydevice, such as a memory card, remotely accessed, or the like.

The processor 1322 implements the analyte analysis using computerreadable software code and data stored in the storage medium 1328. Theprocessor 1322 may start the analyte analysis in response to thepresence of the sensor strip 1304 at the sensor interface 1318, theapplication of a sample to the sensor strip 1304, in response to userinput, or the like. The processor 1322 directs the signal generator 1324to provide the electrical input signal to the sensor interface 1318.

The processor 1322 receives the output signal from the sensor interface1318. The output signal is generated in response to the redox reactionof the ionizable species in the sample. The processor 1322 measures theoutput signal responsive to the amperometric and/or voltammetric dutycycles of the input signal generated from the signal generator 1324. Theprocessor 1322 analyzes the output currents from one or morevoltammetric inputs to determine if one or more interferents are presentin the sample and/or if non-linear response is occurring. The processor1322 then may instruct the signal generator 1324 to adjust the potentialand/or the scan rate of one or more amperometric or voltammetric dutycycles.

The output signal from the adjusted input signal is correlated with theconcentration of at least one ionizable species in the sample using oneor more correlation equations in the processor 1322. The processor 1322may correct the concentration of one ionizable species with theconcentration of another ionizable species. The results of the analyteanalysis may be output to the display 1320 and may be stored in thestorage medium 1328.

The correlation equations between ionizable species and output signalsmay be represented graphically, mathematically, a combination thereof,or the like. The correlation equations may be represented by a programnumber (PNA) table, another look-up table, or the like that is stored inthe storage medium 1328. Instructions regarding implementation of theanalysis may be provided by the computer readable software code storedin the storage medium 1328. The code may be object code or any othercode describing or controlling the functionality described herein. Thedata from the analysis may be subjected to one or more data treatments,including the determination of decay rates, K constants, ratios, and thelike in the processor 1322.

The sensor interface 1318 has contacts that connect or electricallycommunicate with the conductors in the sample interface 1314 of thesensor strip 1304. The sensor interface 1318 transmits the electricalinput signal from the signal generator 1324 through the contacts to theconnectors in the sample interface 1314. The sensor interface 1318 alsotransmits the output signal from the sample through the contacts to theprocessor 1322 and/or signal generator 1324.

The display 1320 may be analog or digital. The display 1320 may be aLCD, a LED, an OLED, a vacuum fluorescent, or other display adapted toshow a numerical reading. Other displays may be used. The display 1320electrically communicates with the processor 1322. The display 1320 maybe separate from the measurement device 1302, such as when in wirelesscommunication with the processor 1322. Alternatively, the display 1320may be removed from the measurement device 1302, such as when themeasurement device 1302 electrically communicates with a remotecomputing device, medication dosing pump, and the like.

In use, a liquid sample for analysis is transferred into the reservoirformed by the reservoir 1308 by introducing the liquid to the opening1312. The liquid sample flows through the channel 1310, filling thereservoir 1308 while expelling the previously contained air. The liquidsample chemically reacts with the reagents deposited in the channel 1310and/or reservoir 1308.

The following definitions are included to provide a clear and consistentunderstanding of the specification and claims.

The term “linear scan” is defined as a voltammetric excitation where thevoltage is varied in a single “forward” direction at a fixed rate, suchas from −0.5 V to +0.5 V to provide a 1.0 V scan range. The scan rangemay cover the reduced and oxidized states of a redox couple so that atransition from one state to the other occurs. A linear scan may becontinuous or may be approximated by a series of incremental changes inpotential. If the increments occur very close together in time, theycorrespond to a continuous linear scan. Thus, applying a change ofpotential approximating a linear change may be considered a linear scan.

The term “cyclic scan” is defined as a voltammetric excitation combininga linear forward scan and a linear reverse scan, where the scan rangeincludes the oxidation and reduction peaks of a redox couple. Forexample, varying the potential in a cyclic manner from −0.5 V to +0.5 Vand back to −0.5 V is an example of a cyclic scan for theferricyanide/ferrocyanide redox couple as used in a glucose sensor,where both the oxidation and reduction peaks are included in the scanrange. Both the forward and reverse scans may be approximated by aseries of incremental changes in potential. Thus, applying a change ofpotential approximating a cyclic change may be considered a cyclic scan.

The term “acyclic scan” is defined in one aspect as a voltammetricexcitation including more of one forward or reverse current peak thanthe other current peak. For example, a scan including forward andreverse linear scans where the forward scan is started at a differentvoltage than where the reverse scan stops, such as from −0.5 V to +0.5 Vand back to +0.25 V, is an example of an acyclic scan. In anotherexample, an acyclic scan may start and end at substantially the samevoltage when the scan is started at most ±20, ±10, or ±5 mV away fromthe formal potential E° ′ of a redox couple. In another aspect, anacyclic scan is defined as a voltammetric excitation including forwardand reverse linear scans that substantially exclude the oxidation andreduction output current peaks of a redox couple. For example, theexcitation may begin, reverse, and end within the DLC region of a redoxcouple, thus excluding the oxidation and reduction output current peaksof the couple. Both the forward and reverse scans may be approximated bya series of incremental changes in potential. Thus, applying a change ofpotential approximating an acyclic change may be considered an acyclicscan.

The terms “fast scan” and “fast scan rate” are defined as a scan wherethe voltage is changed at a rate of at least 176 mV/sec. Preferable fastscan rates are rates greater than 200, 500, 1,000, or 2,000 mV/sec.

The terms “slow scan” and “slow scan rate” are defined as a scan wherethe voltage is changed at a rate of at most 175 mV/sec. Preferable slowscan rates are rates slower than 150, 100, 50, or 10 mV/sec.

While various embodiments of the invention have been described, it willbe apparent to those of ordinary skill in the art that other embodimentsand implementations are possible within the scope of the invention.Accordingly, the invention is not to be restricted except in light ofthe attached claims and their equivalents.

What is claimed is:
 1. A method for identifying an ionizable species ina sample, comprising: applying to the sample an input signal comprisingan acyclic scan, the acyclic scan including a forward excitation and areverse excitation; detecting an output signal, the output signalincluding output currents responsive to the acyclic scan; identifyingthe ionizable species from the output currents responsive to the forwardexcitation of the acyclic scan.
 2. The method of claim 1, furthercomprising taking derivatives of the output currents responsive to theforward excitation of the acyclic scan.
 3. The method of claim 2, wherethe derivatives are sequential.
 4. The method of claim 2, where the signof the derivatives is used to identify the ionizable species.
 5. Themethod of claim 1, further comprising identifying the ionizable speciesfrom a first ratio and a second ratio of the output currents when thesecond ratio is less than
 1. 6. The method of claim 5, furthercomprising reducing a maximum potential of a subsequent acyclic scan inrelation to the maximum potential of the acyclic scan.
 7. The method ofclaim 6, where the maximum potential of the subsequent acyclic scan isreduced until the second ratio is greater than
 1. 8. The method of claim5, where the first ratio is determined from an initial output currentresponsive to the forward excitation of the acyclic scan and a midpointoutput current responsive to the forward excitation of the acyclic scan,and where the second ratio is determined from the midpoint outputcurrent responsive to the forward excitation of the acyclic scan and afinal output current responsive to the forward excitation of the acyclicscan.
 9. The method of claim 1, further comprising: applying to thesample a duty cycle including an amperometric excitation, where theoutput signal further includes output currents responsive to theamperometric excitation; and correlating a portion of the output signalresponsive to the amperometric excitation with a concentration of atleast one analyte in the sample.